Hypothesis Testing

Hypothesis Testing:

Two variables are analysed in this section including the intrinsic and the extrinsic variable, The hypothesis tested is whether the mean of these two variables are equal, the mean value for intrinsic and extrinsic is 5.156 and 4.856 respectively, and this indicates that the one mean value is greater than the other, the variances value are 1.062 and 1.06 for intrinsic and extrinsic respectively, for this reason a hypothesis to test whether the two mean values are different is undertaken. The following is the hypothesis tested:

Hypothesis:

Null hypothesis:

H0:I=E

When this hypothesis is accepted then this means that the two mean values are equal.

Alternative hypothesis:

H1:I≠E

Hypothesis Testing

When the null hypothesis above is rejected then this hypothesis is accepted.

Where “I” is the intrinsic variable mean and “E” is extrinsic variable mean.

Having stated the null and alternative hypothesis the next step is to use excel to test the null hypothesis.

Level of test:

The N value for both variables is equal to 25; the hypothesis is tested at the 0.05 level of significance.

The following table shows the results:

t-Test:  Two-Sample Assuming Unequal Variances

Hypothesis Testing

INTRINSIC

EXTRINSIC

Mean

5.156

4.856

Variance

Hypothesis Testing

1.061733333

1.0559

Observations

25

25

Hypothesized Mean Difference

0

df

48

Hypothesis Testing

t Stat

1.030779747

P(T<=t) one-tail

0.153905095

t Critical one-tail

1.677224197

P(T<=t) two-tail

Hypothesis Testing

0.307810191

t Critical two-tail

2.010634722

The table above summarises the mean and variance values for the two variables, also indicated are the number of observations in each variable, degrees of freedom used in the test, t statistics and T critical.

T statistics value = 1.303077

T critical value (two tail) = 2.0106

From the above figures:

T critical> T statistics

Hypothesis Testing

This null hypothesis is accepted, this is because the T critical value > T statistics value.

Implications:

The hypothesis (H0: I = E) is accepted meaning that the two mean values are equal at the 0.05 significance level.

When to use a t-test and when to use a z-test:

Hypothesis Testing

A T test is used to test hypothesis when the population standard deviation and mean is unknown, this test is mostly used when comparing two sample means and when the sample size is less than 30 observations, when the population standard deviation and mean are known then the Z test is used, the Z test is used to hypothesis that compare two sample means, when comparing proportions and when comparing the sample means and the population mean.

(Murph, 1999)

Why samples are used instead of populations:

Sampling techniques are used to select a number of observations from the population, the appropriate sample size is determined and sampling undertaken, the reason why a sample is used instead of the population is because the sample contains less units to be studied and

Hypothesis Testing

therefore this means that less time will be spent undertaking a study. Also when fewer units are studied then the cost of undertaking research is reduced and therefore sampling is undertaken.

(Clark, 1997)

References:

Downing, D. and Clark, J. (1997). Business Statistics, NJ: Prentice Hall

Sanders, D. and Murph, F (1999). Statistics: a fresh approach, New  York: McGraw hill Press